What is vapour pressure of a solution containing $1 \mathrm{~mol}$ of a nonvolatile solute in $36…

What is vapour pressure of a solution containing $1 \mathrm{~mol}$ of a nonvolatile solute in $36 \mathrm{~g}$ of water $\left(\mathrm{P}_1^0=32 \mathrm{~mm} \mathrm{Hg}\right) ?$
  1. $8.14 \mathrm{~mm} \mathrm{Hg}$
  2. $12.31 \mathrm{~mm} \mathrm{Hg}$
  3. $16.08 \mathrm{~mm} \mathrm{Hg}$
  4. $21.44 \mathrm{~mm} \mathrm{Hg}$

Solution

$\begin{aligned} & \mathrm{n}_2=1 \mathrm{~mol} \\ & \mathrm{n}_1=\frac{36}{18}=2 \mathrm{~mol} \end{aligned}$ Relative lowering of vapour pressure $=\frac{\mathrm{P}_1^0-\mathrm{P}_1}{\mathrm{P}_1^0}=x_2=\frac{\mathrm{n}_2}{\mathrm{n}_1+\mathrm{n}_2}$ $\begin{array}{ll}\therefore \quad & \frac{32 \mathrm{~mm} \mathrm{Hg}-\mathrm{P}_1}{32 \mathrm{~mm} \mathrm{Hg}}=\frac{1}{3} \\ & 96 \mathrm{~mm} \mathrm{Hg}-3 \mathrm{P}_1=32 \mathrm{~mm} \mathrm{Hg} \\ & 64 \mathrm{~mm} \mathrm{Hg}=3 \mathrm{P}_1 \\ \therefore \quad & \mathrm{P}_1=21.33 \mathrm{~mm} \mathrm{Hg} \approx 21.44 \mathrm{~mm} \mathrm{Hg}\end{array}$

Asked in: MHT CET 2023 (11 May Shift 1)

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